/*
* File: UnivariateGaussianMeanBayesianEstimator.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Nov 17, 2009, Sandia Corporation.
* Under the terms of Contract DE-AC04-94AL85000, there is a non-exclusive
* license for use of this work by or on behalf of the U.S. Government.
* Export of this program may require a license from the United States
* Government. See CopyrightHistory.txt for complete details.
*
*/
package gov.sandia.cognition.statistics.bayesian.conjugate;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.statistics.bayesian.AbstractBayesianParameter;
import gov.sandia.cognition.statistics.bayesian.BayesianParameter;
import gov.sandia.cognition.statistics.distribution.UnivariateGaussian;
/**
* Bayesian estimator for the mean of a UnivariateGaussian using its conjugate
* prior, which is also a UnivariateGaussian. This estimation method assumes
* that the variance of the estimated mean is known.
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReference(
author="William M. Bolstad",
title="Introduction to Bayesian Statistics: Second Edition",
type=PublicationType.Book,
year=2007,
pages={208}
)
public class UnivariateGaussianMeanBayesianEstimator
extends AbstractConjugatePriorBayesianEstimator<Double,Double,UnivariateGaussian,UnivariateGaussian>
implements ConjugatePriorBayesianEstimatorPredictor<Double,Double,UnivariateGaussian,UnivariateGaussian>
{
/**
* Default known variance of the estimated distribution, {@value}.
*/
public static final double DEFAULT_KNOWN_VARIANCE = 1.0;
/**
* Creates a new instance of UnivariateGaussianMeanBayesianEstimator
*/
public UnivariateGaussianMeanBayesianEstimator()
{
this( DEFAULT_KNOWN_VARIANCE );
}
/**
* Creates a new instance of UnivariateGaussianMeanBayesianEstimator
* @param knownVariance
* Known variance of the distribution.
*/
public UnivariateGaussianMeanBayesianEstimator(
double knownVariance )
{
this( knownVariance, new UnivariateGaussian( 0.0, 1.0 ) );
}
/**
* Creates a new instance of UnivariateGaussianMeanBayesianEstimator
* @param belief
* Conjugate prior of the posterior belief.
* @param knownVariance
* Known variance of the distribution.
*/
public UnivariateGaussianMeanBayesianEstimator(
double knownVariance,
UnivariateGaussian belief )
{
this( new UnivariateGaussian( 0.0, knownVariance ), belief );
}
/**
* Creates a new instance
* @param conditional
* Distribution from which observations are generated
* @param prior
* Conjugate prior to the conditional distribution
*/
public UnivariateGaussianMeanBayesianEstimator(
UnivariateGaussian conditional,
UnivariateGaussian prior )
{
this( new UnivariateGaussianMeanBayesianEstimator.Parameter(conditional,prior) );
}
/**
* Creates a new instance
* @param parameter
* Bayesian hyperparameter relationship between the conditional
* distribution and the conjugate prior distribution.
*/
protected UnivariateGaussianMeanBayesianEstimator(
BayesianParameter<Double,UnivariateGaussian,UnivariateGaussian> parameter )
{
super( parameter );
}
public UnivariateGaussianMeanBayesianEstimator.Parameter createParameter(
UnivariateGaussian conditional,
UnivariateGaussian prior)
{
return new UnivariateGaussianMeanBayesianEstimator.Parameter( conditional, prior );
}
/**
* Getter for knownVariance.
* @return
* Known variance of the distribution.
*/
public double getKnownVariance()
{
return this.parameter.getConditionalDistribution().getVariance();
}
/**
* Setter for knownVariance.
* @param knownVariance
* Known variance of the distribution.
*/
public void setKnownVariance(
double knownVariance)
{
this.parameter.getConditionalDistribution().setVariance(knownVariance);
}
public void update(
UnivariateGaussian updater,
Double data)
{
final double s2 = this.getKnownVariance();
final double s2hat = updater.getVariance();
final double m = updater.getMean();
final double y = data;
double mhat = (s2*m + s2hat*y) / (s2 + s2hat);
double v2hat = (s2*s2hat) / (s2 + s2hat);
updater.setMean(mhat);
updater.setVariance(v2hat);
}
public double computeEquivalentSampleSize(
UnivariateGaussian belief)
{
return this.getKnownVariance() / belief.getVariance();
}
/**
* Creates the predictive distribution from the given posterior.
* @param posterior
* Posterior from which to create the predictive distribution
* @return
* Predictive distribution from the posterior.
*/
public UnivariateGaussian createPredictiveDistribution(
UnivariateGaussian posterior )
{
UnivariateGaussian conditional =
new UnivariateGaussian( 0.0, this.getKnownVariance() );
return posterior.convolve( conditional );
}
/**
* Parameter of this conjugate prior relationship.
*/
public static class Parameter
extends AbstractBayesianParameter<Double,UnivariateGaussian,UnivariateGaussian>
{
/**
* Name of the parameter, {@value}.
*/
public static final String NAME = "mean";
/**
* Creates a new instance
* @param prior
* Default conjugate prior.
* @param conditional
* Conditional distribution of the conjugate prior.
*/
public Parameter(
UnivariateGaussian conditional,
UnivariateGaussian prior )
{
super( conditional, NAME, prior );
}
public void setValue(
Double value)
{
this.conditionalDistribution.setMean(value);
}
public Double getValue()
{
return this.conditionalDistribution.getMean();
}
}
}